like connecting to the car's own internal Wifi hotspot, which is a whole separate thing from the infotainment's hidden WiFi it uses for CarPlay
It's not completely separate, unfortunately, and I believe this is the heart of the problem people have with iPhone internet connectivity while using wireless CarPlay. If you use a WiFi scanner, you'll see that the car only provides a single WiFi network (well, technically two, one 2.4 GHz and another 5 GHz, but they share the same SSID).
Starting with a phone and car that have never connected to one another, if you pair CarPlay (either using bluetooth or by plugging in), the phone will connect to the car's WiFi to pass CarPlay data back and forth and will
never try to use that connection to connect to the internet. In most cases, this is what everyone wants.
On the other hand, if you
first connect that phone directly to the car's WiFi, it will
always try to use that WiFi connection to get to the internet, even when using CarPlay. If the car doesn't have an active hotspot connection, the phone will no longer be able to get out to the internet to do anything.
The solution is to "forget" the WiFi network and
don't re-add it. Don't try to reconnect to the WiFi network at all. Pair the phone to the car over Bluetooth or a wired connection and let CarPlay handle the WiFi connection automatically in the background. The phone will no longer think it can get to the internet over WiFi and won't keep trying.
There are a few little interface issues, both on the iPhone and on the ID.4, that make this extra confusing. First, the ID.4's "Infotainment as hotspot" setting is misleading. When you turn this off, you're turning off
all WiFi on the vehicle, not just the hotspot, so wireless CarPlay will stop working, too. This makes sense when you consider that the car only provides a single WiFi network. There's no way to "turn it off" as a hotspot while leaving it active for CarPlay.
On the iPhone side, I think it's confusing that it will show WiFi as "Not connected" even while connected to the car for CarPlay. A more technically-correct wording would be "Not connected for internet" as the car and phone
do have an active WiFi connection, but the phone won't try to use that connection to get to the internet. In fact, the car's "Infotainment as hotspot" screen will show the phone as a connected device, even if it's only connected via CarPlay.
One other potentially-confusing thing is that Apple devices sharing the same Apple ID share their WiFi knowledge. So if you once connected your MacBook to the car's hotspot, your phone will also try to connect to that hotspot. This works both ways, so if you forget a network on the phone, it's forgotten on the MacBook, too.